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NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency & Renewable Energy Operated by the Alliance for Sustainable Energy, LLC This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Contract No. DE-AC36-08GO28308
Conference Paper NREL/CP-5D00-72661 February 2019
Data-Driven Preemptive Voltage Monitoring and Control Using Probabilistic Voltage Sensitivities PreprintKumarsinh Jhala,1 Venkat Krishnan,2 Balasubramaniam Natarajan,1 and Yingchen Zhang2
1 Kansas State University 2 National Renewable Energy Laboratory
To be presented at the 2019 IEEE Power and Energy Society General Meeting (IEEE PES GM) Atlanta, Georgia August 4–8, 2019
NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency & Renewable Energy Operated by the Alliance for Sustainable Energy, LLC This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
Contract No. DE-AC36-08GO28308
National Renewable Energy Laboratory 15013 Denver West Parkway Golden, CO 80401 303-275-3000 • www.nrel.gov
Conference Paper NREL/CP-5D00-72661 February 2019
Data-Driven Preemptive Voltage Monitoring and Control Using Probabilistic Voltage Sensitivities
Preprint Kumarsinh Jhala,1 Venkat Krishnan,2 Balasubramaniam Natarajan,1 and Yingchen Zhang2
1 Kansas State University 2 National Renewable Energy Laboratory
Suggested Citation Jhala, Kumarsinh, Venkat Krishnan, Balasubramaniam Natarajan, and Yingchen Zhang. 2019. Data-Driven Preemptive Voltage Monitoring and Control Using Probabilistic Voltage Sensitivities: Preprint. Golden, CO: National Renewable Energy Laboratory. NREL/CP-5D00-72661. https://www.nrel.gov/docs/fy19osti/72661.pdf.
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Data-Driven Preemptive Voltage Monitoring andControl Using Probabilistic Voltage Sensitivities
Kumarsinh Jhala, Student Member, IEEE, Venkat Krishnan, Member, IEEE,Balasubramaniam Natarajan, Senior Member, IEEE, Yingchen Zhang, Senior Member, IEEE
Abstract—Increased penetration levels of distributed variable
renewable generation can cause random voltage fluctuations
and violations at multiple nodes. Traditional methods of voltage
control typically involve reactionary responses of capacitor banks,
tap changers, and recently even smart inverters. But because
of the lack of foresight in voltage violations, these controls
are ineffective to completely mitigate the issue. Therefore, new
methods of predicting voltage violations subject to random power
injection changes in the distribution network are needed, which
can be used to guide optimal and dynamic methods of voltage
control. This work lays the foundation for such preemptive
voltage monitoring and control by proposing an analytical and
sensor data-driven voltage sensitivity analysis method. Driven by
stochastic data and forecasts, the method can be used to develop
probabilistic voltage sensitivities and consequently to predict
system nodes with high likelihood of voltage limit violations.
The effectiveness of this method is tested on IEEE 69-node
distribution system integrated with distributed solar. The results
demonstrate the proposed method’s ability to successfully predict
nodes with high probability of voltage violations for a specific
time-series simulation. The results also demonstrate the ability
to guide timely power injection control actions to mitigate future
voltage violations.
Index Terms—Distributed Generation, Distribution System,
Sensitivity, Sensor Measurement, Voltage
I. INTRODUCTION
The power system is evolving significantly with the prolifer-ation of new smart grid technologies. Increased penetration ofrenewable generation, electric vehicles and active consumersat the grid edge create new challenges as well as opportunities.More specifically, the distribution grid is anticipated to expe-rience random fluctuations in voltages and even ANSI limit
K. Jhala is with the Center for Energy, Environmental, and EconomicSystems Analysis in the Energy Systems Division at Argonne NationalLaboratory (e-mail: [email protected]). This work was done while he was withElectrical and Computer Engineering at Kansas State University.
B. Natarajan is with Electrical and Computer Engineering, Kansas StateUniversity, Manhattan, KS-66506, USA, (e-mail: [email protected])
V. Krishnan and Y. Zhang are with the Sensing and Predictive Ana-lytics Group in the Power Systems Engineering Center of the NationalRenewable Energy Laboratory (NREL), Golden, CO, 80401 USA, e-mail:([email protected]). K. Jhala was also a summer intern at the NationalRenewable Energy Laboratory (NREL) in 2018 summer.
This work was authored in part by the National Renewable EnergyLaboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S.Department of Energy (DOE) under Contract No. DE-AC36-08GO28308.Funding provided by the U.S. Department of Energy Grid ModernizationInitiative (GMI) under the project GMLC 1.2.5 Sensing and MeasurementStrategy. The views expressed in the article do not necessarily represent theviews of the DOE or the U.S. Government. The U.S. Government retainsand the publisher, by accepting the article for publication, acknowledges thatthe U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwidelicense to publish or reproduce the published form of this work, or allowothers to do so, for U.S. Government purposes.
violations under higher penetrations of rooftop photovoltaics(PV) [1], [2]. Traditional methods of voltage control such ason-load tap-changing transformers, voltage regulators and ca-pacitor banks are not designed for bi-directional current flow,and typically are controlled to provide reactive support afteran event is detected [3]. Additionally, under increasing levelsof variable renewable, sole dependence on the installation ofmore traditional voltage control devices may not be viable [4],[5]. Therefore, extensive research have looked into utilizingthe reactive power capabilities of PV systems by integratingthem via smart inverters under either centralized [6]–[10] ordecentralized [11]–[13] control approaches. IEEE 1547 (2018)standards and utilities have also begun to look into such smartinverter options to mitigate voltage violations. Studies [14]have shown Volt-Var and Volt-Watt options provide much-needed grid support; however, these strategies also providereactionary support post-event, and testing studies [15] haveshown them to not eradicate voltage violations completelygiven the maximum allowable limits of reactive power pro-visions and/or real power curtailments.
Therefore, a computationally efficient preemptive voltagecontrol mechanism is needed that predicts future voltageand their uncertainty bounds and guides preventive actionsin power distribution systems interconnected with renewablegeneration. This paper considers a power distribution systemwith multiple active consumers with flexible load and gen-eration participating in demand response program with third-party aggregators. Goal of this work is to develop a data-driven approach to predict nodes with high probability ofvoltage violation and devise a preemptive control action bymodifying consumer load/generation to prevent steady-statevoltage violations.
In order to predict voltage responses, this paper assumesthe availability of voltage and power measurements from allnodes in the distribution system, and uses them to estimateprobabilistic sensitivities of node voltages with respect toreal and reactive power injection changes at various nodes.The probabilistic sensitivities will be used to dynamicallypredict nodes with high probability of voltage violations [16],[17] as well as mitigate them using a preemptive controlstrategy that modifies nodal injections (load/generation). Majorcontributions of this paper are listed below.
• Develops an analytical expression to compute the upperbound of change in voltage resulting from change incomplex power at multiple nodes [16], which is compu-tationally efficient and dynamic with use of sensor data.
• Provides a probabilistic voltage sensitivity analysis-based
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2
method that predicts probability of future voltage subjectto forecasts and detects highly vulnerable nodes (sec. III).
• A simple preemptive voltage control mechanism in IEEE69-node system where the accuracy and effectiveness ofvoltage prediction and control is tested. (section IV).
II. BACKGROUND: VOLTAGE SENSITIVITY ESTIMATION
Voltage sensitivity analysis estimates change in complexvoltage at a given node (observation node o) due to change incomplex power at another node (actor node a) in a power dis-tribution system. Traditionally, voltage sensitivity is calculatedusing Newton-Raphson load flow method (from the Jacobianor its eigenvectors) or perturb-and-observe method [18]. Bothmethods are numerical and computationally complex. Thissection presents an analytical upper bound for voltage changeat an observation node (�V
o
) due to change in complex powerat an actor node (�S
a
) in a radial distribution network forconstant power model of loads, originally developed in [16].When an actor node (a) changes its complex power from S
a
to S
a
+ �S
a
, voltage at the observation node changes fromV
o
to V
o
+�V
oa
, which can be calculated from Theorem 1.Here �V
oa
is change in complex voltage at the observationnode o due to change in complex power at the actor node a.
Theorem 1. For a radial power distribution network, change
in voltage at an observation node due to change in power of
an actor node is upper bounded by
�V
oa
��S
a
Z
oa
V
⇤a
, (1)
where V
⇤a
is complex conjugate of voltage at the actor node;
and Z
oa
is impedance of shared line between the observation
node o and the actor node a from the source node.
Proof. see [16]
Here, inequality sign for complex number indicates theupper bound on real and imaginary values. Equation (1)provides a linear upper bound on generally non-linear powerflow calculations. This notation is used throughout the paper.Effect of multiple actor nodes on the observation node voltagecan be calculated using the following lemma.
Lemma 1. Superposition Law: If A is a set of actor nodes
in the network, effective change in complex voltage at the
observation node due to the cumulative effect of all the actor
nodes is bounded by (2).
�V
o
X
a2A
��S
a
Z
oa
V
⇤a
, (2)
where A is set of all the actor nodes.
Proof. see [16]
This lemma proves that the proposed analytical method rep-resented by (2) holds the law of superposition. The analyticalequation derived in Lemma 1 can be used to calculate theprobability distribution of voltage change at any given nodein the power distribution system. Calculating sensitivity matrixfor the IEEE 69-node test system using the classical load-flow method takes 4.52 seconds, whereas using the proposed
analytical method takes only 0.58 seconds [16]. This paperfurther advances the application of these sensitivities for dy-namic prediction of future power states, by integrating phasordata from sensors and renewable forecasts. Impact of sensingerrors are not considered.
III. PREEMPTIVE ANALYSIS: PREDICTION AND CONTROL
The analytical sensitivity estimation method presented inSection II is used as the basis for developing data-drivenprobabilistic voltage sensitivity analysis for predicting theprobability of voltage violation at a given node. We make anassumption that complex power and voltage measurements (orestimations) are available at each node of the balanced threephase distribution system in real time.
Random changes in power drawn/injected by active con-sumers with renewable generation cause random voltage fluc-tuations, which makes voltage at any given node in the distri-bution system random. This work assumes normal distributionfor power injection changes. Let V
p
o
be current value ofcomplex voltage at any observation node o, which is obtainedfrom measurements or state estimation, and V
f
o
representthe predicted future complex voltage at node o. Due to thevariability and uncertainty introduced by renewable generationin power system, V f
o
is random and can be written as:
V
f
o
= V
p
o
+�V
o
, (3)
where �V
o
is random change in complex voltage at obser-vation node due to random changes in net power injections.Change in real and imaginary part of voltage at an observationnode due to change in complex power at an actor node canbe written as:
�V
oa
= �V
r
oa
+ i�V
i
oa
, (4)
where
�V
r
oa
= � 1
|Va
| (�P
a
(R
oa
cos ✓
a
�X
oa
sin ✓
a
)
��Q
a
(R
oa
sin ✓
a
+X
oa
cos ✓
a
)) ,
(5)
and
�V
i
oa
= � 1
|Va
| (�Q
a
(R
oa
cos ✓
a
�X
oa
sin ✓
a
)
+�P
a
(R
oa
sin ✓
a
+X
oa
cos ✓
a
)) .
(6)
From superposition law (Lemma 1), change in voltage at anobservation node due to cumulative effect of multiple actornodes can be written as sum of changes in voltage at theobservation node due to every actor node.
�V
o
=
X
a
�V
oa
=
X
a
�V
r
oa
+ i
X
a
�V
i
oa
, (7)
Behavior of nodal net-loads in a distribution network in-tegrated with variable renewables can be modeled as randomvariables. In this work, change in real and reactive power injec-tions at a distribution system node is modeled as Gaussian ran-dom variable. Let �S = [�P
1
, · · · ,�P
n
,�Q
1
, · · · ,�Q
n
]
T
be a Gaussian random vector with mean µ and covariance
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3
matrix ⌃. Here, mean of real and reactive power reflects fore-cast of future net-load changes (i.e., estimated using load andrenewable generation forecasts). The covariance matrix willbe estimated using historical data, supplemented with prob-abilistic forecasts that provide variances of forecasts aroundthe mean [19]. The cross-correlations could be estimated bygenerating scenarios of random forecasts for various locations,and estimating their cross-correlations. Additionally, the effectof spatial correlation of variable renewables is captured bythe off-diagonal elements of the covariance matrix. Detailedmodeling of variability and uncertainty in the voltage sensi-tivity assessment is beyond the scope of this paper, but willbe undertaken for future work.
A. Computing Voltage Sensitivity Probability Distribution
Given the normal distribution assumption for power injec-tion changes, the resultant voltage sensitivity is also expectedto be normally distributed due to their linear relationshipmodeled by equations (5) and (6) [20]. This section furtherelaborates the estimation of |�V
o
| distributions using follow-ing steps:
1) Define ⌃, and compute vectors Cr
and Ci
:
⌃ =
2
666664
�
2p1 · · · cov(pn, p1) cov(q1, p1) · · · cov(qn, p1)
.
.
.. . .
.
.
.
.
.
.. . .
.
.
.cov(p1, pn) · · · �
2pn
cov(q1, pn) · · · cov(qn, qn)
cov(p1, q1) · · · cov(pn, q1) �
2q1 · · · cov(qn, p1)
.
.
.. . .
.
.
.
.
.
.. . .
.
.
.cov(p1, qn) · · · cov(pn, qn) cov(q1, qn) · · · �
2qn
3
777775
(8)where n is number of nodes in the network. For nodes that donot have PV, values of variance can be set to zero. In this work,we assume that network topology is known. Value of complexbus voltages is gathered from measurements and values of lineimpedance are assumed to be known from network topology.The vectors C
r
and C
i
are defined and computed as follows,using equations (9) and (10). Values of C
r
and C
i
can becomputed as following.
Cr
=
2
6666666664
�R
o1 cos ✓1�X
o1 sin ✓1|V1|...
�R
on
cos ✓
n
�X
on
sin ✓
n
|Vn
|R
o1 sin ✓1+X
o1 cos ✓1|V1|
...R
on
sin ✓
n
+X
on
cos ✓
n
|Vn
|
3
7777777775
, (9)
Ci
=
2
6666666664
�R
o1 sin ✓1+X
o1 cos ✓1|V1|...
�R
on
sin ✓
n
+X
on
cos ✓
n
|Vn
|�R
o1 cos ✓1�X
o1 sin ✓1|V1|...
�R
on
cos ✓
n
�X
on
sin ✓
n
|Vn
|
3
7777777775
. (10)
2) Compute distribution of �V
r
o
and �V
i
o
: Real and imag-inary part of change in voltage at an observation node can bewritten as weighted sum of elements of vector �S as depicted
by equation (11) and (12). Weighted sum of Gaussian randomvariables are normally distributed. Therefore, probability dis-tribution of �V
r
o
and �V
i
o
can be derived as follows
�V
r
o
=
X
a
�V
r
oa
= CT
r
�S ⇠ N(CT
r
µ,CT
r
⌃Cr
) (11)
�V
i
o
=
X
a
�V
i
oa
= CT
i
�S ⇠ N(CT
i
µ,CT
i
⌃Ci
) (12)
3) Define bi-variate normal vector
ˆ�Vo
: Covariancebetween �V
r
o
and �V
i
o
can be written cov��V
r
o
,�V
i
o
�=
CT
r
⌃Ci
. Therefore, the change in real and imaginary part ofvoltage change will be a bi-variate normal vector, i.e.
�Vo
,�V
r
o
�V
i
o
�⇠ N (µ
1
,⌃1
) (13)
where,
µ
1
=
CT
r
µ
CT
i
µ
�,⌃
1
=
CT
r
⌃Cr
CT
r
⌃Ci
CT
r
⌃Ci
CT
i
⌃Ci
�(14)
4) Calculate probability distribution of Vf
o
: Let Vf
o
bevector of real and imaginary part of future voltage at nodeo defined as:
Vf
o
,V
rf
o
V
if
o
�=
V
rp
o
V
ip
o
�+
�V
r
o
�V
i
o
�(15)
Voltage at observation node in next time slot Vf
o
can be writtenas Gaussian random vector as following.
Vf
o
⇠ N
✓V
rf
o
+CT
r
µ
V
if
o
+CT
i
µ
�,
CT
r
⌃Cr
CT
r
⌃Ci
CT
r
⌃Ci
CT
i
⌃Ci
�◆(16)
The covariance matrix, voltage measurements and fore-casted change in mean power injections will be updated asnew forecasts and sensor data are available. This processwill be continued for future estimations of voltage at someregular time intervals (though in this work, for a given timeseries simulation, such an update is not done for simplicity ofillustration).
B. Detecting Vulnerable Nodes and Preemptive Control
Equation (16) shows that |V f
o
| is Gaussian random variablewith numerically computed mean and variance, which can beused to find probability of voltage violation. Let P
o
(t) be theprobability of voltage violation at node o at time t defined as:
Po
(t) = 1� P (0.95 < |V f
o
| < 1.05). (17)
Performing this calculation for each node in the distributionsystem, we can identify nodes that have probability of voltageviolation. After identifying nodes that are highly vulnerableto voltage violation an effective voltage control action canbe taken. To test effectiveness of the proposed method, avoltage sensitivity-based heuristic voltage control approachis considered, where an upper bound on maximum powerdrawn/injected is enforced for nodes that are vulnerable tovoltage violation. In a case where node is vulnerable to high-voltage violation, amount of power injected by the node into
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4
the grid is upper bounded by x% of current power injection forfuture time period. Similarly, in a case where node vulnerableto low-voltage violation, amount of power drawn from the gridis upper bounded by x% of current power for future time pe-riod. The amount of power injection change is estimated basedon voltage sensitivity information. Let N(t) be set of nodesthat are vulnerable to voltage violation at time t, and �V
t
be voltage change required to mitigate voltage violation atnode with highest/lowest voltage in case of over/under-voltageviolations in the neighborhood. Eliminating highest voltageviolation should result in elimination of voltage violation atmost of the nodes in the neighborhood. This procedure will beundertaken iteratively until a premptive power injection controlstrategy for eliminating all violations is estimated. To ensurefairness between nodes, generation at all nodes is reduced bysame amount. Percentage load/generation curtailment can becomputed as following:
�V
t � �X
a2N
xS
a
Z
oa
V
⇤a
(18)
x � �V
t
Pa2N
S
a
Z
oa
V
⇤a
(19)
Here �V
t is selected such that the probability of voltageviolation (equation (17)) is less than the threshold used toidentify nodes that have high probability of voltage violation.In ideal situation, an optimal control strategy will utilize thisalgorithm to estimate the time for which such power injectionchange has to be done. But an optimal control strategy isbeyond the scope of this paper. However to show the value ofhaving voltage violation foresight, we impose a simple 2-hourtime period over which the estimated power injection changeswill be implemented.
IV. SIMULATION AND RESULTS
To test proposed voltage violation prediction algorithm anIEEE 69 bus test system is considered [16]. Synthetic sensordata is produced using power flow solutions. A hypotheticalscenario is considered from noon to 6 p.m. with voltage andpower data available every 5-minute interval. MicroPMUsand other distribution level sensors are capable of providingvoltage and power measurements at higher rate; however, forsimplicity of demonstration 5-minute interval is considered.Roof top PVs in 20 nodes with varying generation capacityare considered. Solar generation is modeled as random processwith some trend and seasonality components that reflect realworld scenario as shown in equation (20) [21]–[24].
P
solar
(t) = S(t) + n
s
(t) (20)
Here, S(t) is PV generation mean forecast trend, and n
s
(t) iszero mean Gaussian random variable that models variabilityand uncertainties. Gaussian random noise in solar generation iscorrelated across different nodes to reflect spatial correlation ofsolar generation. In this simulation, synthetic solar generationdata is generated dynamically to reflect real world scenario.Correlation coefficient of solar generation is chosen as 0.7.Load at each node is synthetically produced based on typical
12.00 PM 1.00 PM 2.00 PM 3.00 PM 4.00 PM 5.00 PM 6.00 PMTime of the Day
-400
-200
0
200
400
600
Pow
er (k
W)
Total Residential LoadTotal Solar GenerationNet Power
Fig. 1: Total load and generation
load profile of residential household. Figure 1 shows load,solar generation and net power of the distribution system. Thefigure shows that load is lowest and PV generation is highestat noon resulting in negative net power. This reverse powerflow causes high-voltage violations in parts of the distributionsystem. For simplicity, this work considers a scenario whereno low-voltage violations occur. However, the proposed pre-emptive voltage control algorithm is general enough to applyin case where high or low-voltage violations occur.
The aggregator receives power injection and voltage mea-surements at all nodes. This information along with busimpedance data is used to compute voltage sensitivity ma-trix using proposed analytical method of voltage sensitivityanalysis discussed in section II in a computationally efficientmanner. The mean and variance of real and imaginary partof voltage change at each node is estimated analyticallyas shown in section III. Vectors C
r
and Ci
are computedbased on network topology and synthetic measurement data.Covariance matrix ⌃ is estimated based on probabilistic vari-ance of historical data. Based on node voltage measurementsand calculated probability distribution of voltage change, theprobability of high and low-voltage violation is computednumerically. Nodes that have probability of voltage violationgreater than threshold are classified as highly vulnerable nodesfor voltage violation perspective. In this illustration, nodesthat have probability of voltage violation more than 50% areconsidered as highly vulnerable. Number of voltage violationin the system every time slot are shown in Figure 2 by bluebars. Red stem plot in Figure 2 shows number of voltageviolations predicted by proposed method, based on nodes withprobability of voltage violation greater than 50%. The pro-posed method predicts nodes vulnerable to voltage violationaccurately, thereby giving a foresight to system operators foroptimal control.
To demonstrate preemptive control, a voltage sensitivitybased heuristic voltage control method is used. An upperbound on power injected into the grid is enforced for nexttwo hours for nodes that are identified as highly vulnerableto voltage violations. Value of upper bound is calculatedusing equation (19), which is 65% of power injected intothe grid. Figure 3 shows voltage at node 65 of IEEE 69bus test system with and without (no foresight or prediction)preemptive voltage control. Figure 3 shows that proposedmethod successfully eliminates high-voltage problems.
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5
12.00 PM1.00 PM 2.00 PM 3.00 PM 4.00 PM 5.00 PM 6.00 PMTime of the Day
0
2
4
6
8
10N
umbe
r of V
otla
ge V
iola
tion
Actual Number of Voltage ViolationsPredicted Number of Voltage Violation
Fig. 2: Number of voltage violations
12.00 PM 1.00 PM 2.00 PM 3.00 PM 4.00 PM 5.00 PM 6.00 PMTime of the Day
.095
0.975
1.0
1.025
1.05
1.075
Vol
tage
(p.u
.)
Voltage after controlVoltage without any control
Fig. 3: Voltage at node 65 before and after control
V. CONCLUSION AND FUTURE-WORK
This paper develops a preemptive voltage control methodthat mitigates voltage violation in a power distribution systemwith renewable generation by taking a control action beforeactual voltage violation. This paper uses an analytical methodof voltage sensitivity analysis with phasor measurements andnodal power injection forecasts to compute probability offuture voltage violations. With this foresight, vulnerable nodesprone to voltage violations are detected (greater than certainprobability of voltage violation), and appropriate power injec-tion control actions can be taken. The paper illustrated a simplepreemptive control approach that is capable of mitigatingfuture voltage issues altogether, thereby laying the founda-tion for future investigations on real-time optimal controlstrategies. Related future work will also include improvingvoltage sensitivities prediction using empirical probabilities(rather than gaussian distributions) and developing methods toensure complete system observability even under sparse sensorproliferation scenarios.
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5This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
